What is the derivative of a unit vector?
The derivative of any vector whether it is unit or not is simply the derivative of each component in the vector. If you have some vector valued function r(t) for example which you divide by its magnitude to obtain a unit vector, the derivative is simply a vector :(derivative of the x component, the derivative of the y component)/IIr(t)
If the unit vector is just a number ( given) then obviously the derivative is 0.
In summary, to get a unit vector divide the vector by its magnitude. To find the derivative, take the derivative of each component of the vector separately. That will give you the new vector. This works for functions of more than two dimensions as well.
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The derivative of a unit vector depends on whether the unit vector is constant or variable.

If the unit vector is constant, its derivative is zero.

If the unit vector is variable and defined as (\mathbf{u}(t)), where (t) represents time or another parameter, then its derivative (\frac{d\mathbf{u}}{dt}) is tangential to the curve traced out by the unit vector and represents the rate of change of the direction of the vector with respect to (t).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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